The physics behind the “non-Hermitian”
theory acquires the universal, \(K-\) independent
CHSP form,
with its various
phenomenological aspects extensively discussed in Ref. [1]}.
In our present notation
one merely
represents
\({\cal H}_{phys}={\cal R}_{0}\)  in \({\cal R}_{N_{}}\) 
using a formal replacement
of the trivial metric in \({\cal R}_{N_{}}={\cal H}_{math}\) 
by
its
amended physical alternative.
This enables us to work, simultaneously, with
the two inner products
such that
\(\langle _{} \psi _a|\psi _b\rangle =\langle _{[N_{}]} \psi _a|\psi _b\rangle \ne \langle _{[0]} \psi _a|\psi _b\rangle =\langle _{[N_{}]} \psi _a|\Theta |\psi _b\rangle =\langle _{} \psi _a|\Theta |\psi _b\rangle \,,\) 
